相关论文: On Hadamard Conjecture

The probability that the commutator of two group elements is equal to a given element has been introduced in literature few years ago. Several authors have investigated this notion with methods of the representation theory and with…

We prove a conjecture by Guo-Niu Han which interpolates between two known hook expansion formulas.

Robin's Conjecture is strengthened, deformed, and proved. Nicolas conjecture follows.

In 2005, Watanabe and Yoshida formulated a conjecture for a lower bound of the Hilbert-Kunz multiplicity of local rings that was recently settled by Meng using analytic methods. More recently, Pak-Shapiro-Smirnov-Yoshida used Ehrhart theory…

The article presents the proof of Casas-Alvero conjecture.

This is a presentation of recent work on quantum permutation groups, complex Hadamard matrices, and the connections between them. A long list of problems is included. We include as well some conjectural statements, about matrix models.

In 1904, Dickson [5] stated a very important conjecture. Now people call it Dickson's conjecture. In 1958, Schinzel and Sierpinski [14] generalized Dickson's conjecture to the higher order integral polynomial case. However, they did not…

We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.

We show the flaw in a theorem of Konno, Namiki, Soshi, and Sudbury in [3] and provide the necessary correction in the case of the Finite Hadamard walk and use it to show that a conjecture of Ambainis, Bach, Nayak, Vishwanath, and Watrous in…

In this paper, we prove a conjecture of Schnell in the surface case.

Remarks on mathematical proof and the practice of mathematics.

This is a survey on Kawaguchi-Silverman conjecture.

In this paper we establish an exponential covering theorem implying a conjecture formulated by A. Zygmund circa 1935 whose three-dimensional case was obtained by the first named author in 1978.

The paper surveys the history and state-of-the-art of the study of Jordan homomorphisms.

This is a survey paper on Geometric Manin's conjecture which was proposed by Brian Lehmann and the author. We introduce Geometric Manin's conjecture (GMC) and review some recent progress on this conjecture.

Hadamard's determinant inequality was refined and generalized by Zhang and Yang in [Acta Math. Appl. Sinica 20 (1997) 269-274]. Some special cases of the result were rediscovered recently by Rozanski, Witula and Hetmaniok in [Linear Algebra…

In a recent paper published in the Philosophical Magazine [Z.-D. Zhang, Phil. Mag. 87, 5309-5419 (2007), arXiv:0705.1045], the author advances a conjectured solution for various properties of the three-dimensional Ising model. Here we…

This is a Bourbaki report on the work of Y. Andr\'e on the direct summand conjecture, and subsequent developments by Andr\'e and Bhatt on big Cohen-Macaulay algebras.

We show that many ancient Indian mythological legends are really allegorical depictions of astronomical and other physical phenomena of which the composers had a good idea. This detail enables us to also use techniques of astronomical…

Convolutions or Hadamard products of analytic functions is a well explored area of research and many nice results are available in literature. On the other hand, very little is known in general about the convolutions of univalent harmonic…